ANALYZING THERMAL PERFORMANCE OF BUILDING ENVELOPE COMPONENTS USING 2-D HEAT TRANSFER TOOL WITH DETAILED

RADIATION MODELING

Dragan Curcija1, Dariush Arasteh2, Charlie Huizenga3, Christian Kohler2, Robin Mitchell2,Mahabir Bhandari1

1University of Massachusetts, Amherst, MA 01003, USA 2Lawrence Berkeley National Laboratory, Berkeley California, CA 94720, USA

3University of California, Berkeley California, CA 94720, USA

ABSTRACTTHERM is a freely available, user-friendly two-dimensional heat transfer model for analyzing theimpacts of thermal bridges in building componentssuch as windows and doors. This paper begins bydescribing THERM as a tool for analyzing individualbuilding components as well as envelope assemblies.The significance of THERM�s detailed radiation heattransfer model, which incorporates a view factorbased radiation heat transfer algorithm, is thenpresented in detail. Radiation heat transfer plays a significant role in projecting building components(i.e., Greenhouse windows, skylights, etc.), and projecting wall sections. The difference betweenresults using a traditional black body assumption andthe detailed radiation model can be as high as 30%..INTRODUCTIONTHERM�s (Finlayson et al., 2000) two-dimensionalconduction heat transfer analysis is based on thefinite element method, which can model complicatedgeometries of building products. The program�sgraphic user interface allows one to draw crosssections of products or components to be analyzed. Itincorporates basic CAD capabilities, so that buildingcomponent cross sections can be easily created froma dimensioned drawing. The program also has thecapability of importing CAD drawings through a DXF file format, and can also read the bitmap (.bmp)file format as an underlay (i.e., trace-over). THERM uses a radiation view factor algorithm, VIEWER,which is a derivative of the public domain computerprogram FACET (Shapiro, 1983). This featureenhances the program�s accuracy by modelingelement to element radiation heat transfer directly.This is particularly significant for products with self-viewing surfaces at temperatures that are differentthan the temperature of the surrounding air. Radiation heat transfer constitutes more than a halfof the total surface heat transfer coefficient for surfaces that are subject to natural convection. Significant variations in radiation heat transfer cantherefore significantly affect the overall rates of

surface heat transfer and correspondingly the overallU-factor of a building envelope component.

Typical examples of products that incorporate self-viewing surfaces are projecting fenestration products(e.g., green house windows, skylights, curtain wallsystems, etc.) In addition to products themselves,integrated assemblies (i.e., window-wall interface)create locally significant areas that are self-viewing (see Figure 2). Currently, windows are beingaccounted for in building simulation models (DOE2.1E, 1994, EnergyPlus, 2000) as �nodes�. Eachnode has associated Area, U-factor, SHGC, and VT. There is no consideration about how windows affectneighboring wall assemblies and vice versa. Two-dimensional (2-D) heat transfer effects at the window-wall interface are currently ignored in building simulation models.

While the window products are tested in a laboratorywith fixed environmental conditions, and installed in an insulating homogenous wall, their actual U valuemay differ in the actual environment (i.e. when theyare assembled with other building components).Previous studies have shown that THERM can accurately predict thermal performance of building components (Griffith et al., 1998, Arasteh et al.,1998 and Huizenga et al., 1999). This paperdemonstrates the capability of THERM as an analysis tool for the more accurate prediction ofthermal performance of building components, as installed in real buildings.

METHODOLOGYIn this paper, building components have beenanalyzed starting from a simple window assembly astested in laboratory to a real situation in which a window is located in the wall of a room. The analysishas further been extended to include THERM�sdetailed radiation view-factor algorithms. Fig 1shows the typical cross section of a window sill. Theexample window, used in this analysis is an Aluminum clad, wood casement window. Theglazing system consists of nominal 25.4mm thick

Seventh International IBPSA ConferenceRio de Janeiro, Brazil

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insulating glass unit (IGU) with a nominal 15.7mmair space and 0.04 emissivity low-e coating on surface number 3 (surfaces are numbered from theoutside in). Thermo physical properties of materialsused are given in Table 1.

For rating and product comparison purposes in theUS, the National Fenestration Rating Council(NFRC) specifies that this window be modeled with THERM as if it were installed in the well insulatedsurround panel of a hot box, located in a controlledlaboratory environment (NFRC 1997). In thesoftware model, this configuration is modeled as anadiabatic boundary condition at the bottom of theframe (see Figure 1). In addition, computermodeling of 2-D heat transfer is done only on theframe profile and an adjacent short portion of theglazing system, called the edge-of-glass. This isdone to simplify the analysis of the whole window,because for the rest of the glazing system, the heat transfer is considered to be 1-D. This center-of-glassregion is easily modeled as a set of nodes,corresponding to glazing layers and surfaces. The total product�s overall U-factor is calculated as anarea weighted average of frame, edge-of-glass and center-of-glass sections.

In reality the window is assembled in a wall, whichhas non-homogenous elements and/or thermalbridges. The typical wall cross section and interfacewith the window is shown in Figure 2. In addition to thermal bridging effects, which are reflected inincreased conduction heat transfer rates, the extendedsill, jamb, and head surfaces affect radiation heattransfer. To properly account for these effects, the 2-D conduction and radiation heat transfer model inTHERM is used on complete window cross sections(Arasteh et al., 1998).

This analysis has been further extended for morerealistic conditions by placing this window in thewall of a 4.6m x 4.6m x 2.4m room. The roomconsists of two internal walls and two external walls, with two different configurations, one with thewindow in the other external wall, and the otherwithout. The floor plan and elevation of the room are given in Fig. 3. The wall is assumed to be typicalNorth American framed wall construction, with 2x6studs, and plates, insulation in-between, wood sidingon outdoor side and gypsum wall on indoor.

RESULTS AND DISCUSSIONSThe NFRC also specifies standard environmentalconditions for the purposes of rating fenestrationproducts (NFRC 1997). Since test conditions aremimicked in a simulation program, correlations areused to model wind speed on the cold side of the hotbox and natural convection on the warm side.Standard conditions in United States are: the outdoorand indoor temperatures are assumed at -17.8oC and

21.1oC respectively, while the wind speed on thecold side is approximately 6.7 m/s. Thecorresponding cold side surface heat transfercoefficient is 29.03 W/m2K, while the warm sidecoefficient depends on the product tested andlaboratory hot box setup, but it is typically around7.6 W/m2K. Fig. 4 shows the isotherms and Uvalues calculated using this set of conditions and theNFRC simulation procedure (NFRC 1997).

When this same cross section is simulated as a partof a window-wall assembly (see Figures. 4 and 5),the U-factor of the frame increases from 2.68 W/m2Kfor the �rating� configuration to 3.94 W/m2K for theactual window-wall configuration. For the wholewindow the U-factor increases from 2.04 W/m2K to 2.28 W/m2K. This shows that the performance of awindow can drastically change in the actualenvironment. This increase can be attributed to twodifferent effects; one is the thermal bridgingintroduced by the presence of wood plates at the window-wall interface, and the other is increasedexposed area on the outdoor (cold) side of a window.This discrepancy is not necessarily bad, because weuse rated performance parameters to compareproducts. However, if we routinely use these ratingnumbers to simulate building energy performance,(which we currently do), then there is a problemwhich needs to be addressed.

On the other hand, the introduction of more accurateradiation modeling will further affect calculated U-factors. The radiation module in THERM is used toexamine the effect of surfaces at differenttemperatures radiating to one another (ISO 15099,Arasteh et al, 1998). Two different cases wereanalyzed, (1) a window-wall interface, without anyeffects of surrounding walls, and (2) a window-wallassembly as a part of a room.

For the model of the window-wall interface, thesurrounding enclosure was considered to be a black body at the room temperature, while the window and wall surfaces were assigned surface emissivities (0.9 for all surfaces except glass which is 0.84). Theprogram calculates view factors and surfacetemperatures. Because of the dependence of radiation to the fourth power of temperature, themodel is highly non-linear, and occasionally requiresa relaxation parameter to be introduced in order toachieve convergence. From Table 2, one canobserve that the overall U-factor has significantly dropped for the model with the use of a detailedradiation enclosure. This is the result of reducedradiation exchange between self-viewing surfaces.

For the model of a wall-window assembly as a part of a room, a smaller cross sections was modeled,while the reminder of the room was modeled throughthe use of a radiation enclosure. This was done

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because of prohibitively excessive mesh size that would result if conduction and radiation were modeled for the entire room. Because we werelooking at the performance of a fenestration system-wall assembly in a room enclosure, the window-wall assembly was cut at the point where 2-D heattransfer effects were not dominant any longer. Inthis case, the glazing was extended 4 in., while thewall was extended 6 in. below wood studs. FromFigure 6, it is clear that the isotherms are paralleltoward the end, indicating that heat transfer is essentially 1-D. A further extension of the modelwould not improve the accuracy any more. The wall and other window surfaces were represented by theiremissivity and estimated temperature (see Figure 7). The temperature was estimated from the 1-D models,and that represents good assumption in this model.

Each of the building components in the room couldbe modeled in the same way, and its corrected temperature used in refining estimated radiation temperature, which in turn would produce refinedtemperature fields and U-factors for a Window-wallassembly. This process could be repeated untilsatisfactory convergence is obtained. In this work, the very first iteration produced insignificantchanges, so further iteration were not done.

The model of the room with a window is given inFigs. 7 and 8. The temperature of the ceiling andfloor were estimated. . In Fig. 7, top and bottomsides represent the ceiling (T=21.1C) and floor (T=17.8C) respectively. The temperature for the wallat which window is situated has been calculated byTHERM and another wall has been consideredinternal and assumed at 20oC. Similarly for the case in Fig 8, top and right walls were considered internalwalls (T=20C) and left and bottom sides are assumedas external walls for which the temperatures havebeen calculated by THERM. Calculations for thecase in Fig 8 have also been performed byintroducing the second window at the wall at the left side. The results for all these cases have beensummarized in Table 2.

It is interesting to observe that the U-factor of a sill cross-section and of the whole window hassignificantly increased for the case where thewindow is installed in a real wall. Introduction of aradiation model and addition of the realistic radiationboundaries in a room has the effect of decreasing theoverall heat transfer, but the total U-factor is still significantly higher than for the basic �rating� case.For this higher performance window, the overalldiscrepancy was on the order of 5% (For theindividual frame U-factors this difference is as highas 30%). For lower performing windows, and lessinsulating wall structures, this difference is expectedto go over 10%. It should be noted that additionalheat flow that occurs in a wall section due to a

presence of window-wall interface had not beencounted. It is expected that this effect will furtherincrease U-factors and therefore increase thediscrepancy between laboratory determined and realworld U-factors.

CASE SUDY: SIMULATION OF A SKYLIGHTAlthough skylights are sometimes installed at a tilt,and it is possible to model tilted products in THERM, for NFRC certified simulations, skylightsare modeled in the vertical direction in order tomatch the conditions under which they were tested.In THERM, skylights are modeled as full-heightproducts with a radiation enclosure surrounding theinterior of the product in order to take full advantageof the modeling capabilities of the radiationenclosure feature. Fig. 9 shows a typical sill sectionof the skylight.

The skylight is also simulated using the detailedradiation model, under the standard NFRC ratingconditions. For this product, the roof-skylightinterface was not analyzed, but it is believed that thegeneral trends, observed for the �flat� window wouldapply, although somewhat magnified because of theprojecting nature of the product itself.

The results from the THERM and WINDOW (LBL 1994) simulations were combined into the overall U-factor of the skylight. Fig. 10 shows isotherms andU-factors of a skylight using the radiation model.The overall U factor for the skylight is 3.18 withoutusing the radiation model while it is 2.99 with theradiation model. The radiation model has reducedthe overall U-factor by about 7%.

CONCLUSIONSThe importance of accurate radiation modeling whenanalyzing heat transfer in building assemblies hasbeen demonstrated. The effects of radiation heattransfer in fenestration systems where there is significant self viewing between projecting surfaces(e.g., between frame and glazing) can be significantand, depending on particular geometry and materialsused, can greatly affect both local and overall heattransfer results. The difference between results usinga traditional black body assumption and the detailedradiation model varies between a couple of percentup to 25%. The use of this 2-D detailed radiationmodel in THERM has contributed to increasedaccuracy when such products are simulated and ratedin North America. The results obtained from theTHERM and WINDOW programs can be used inbuilding simulation models such as DOE2 fordetailed and accurate energy analysis.

Future work should provide guidance how such toolscan effectively be used as a part of advancedbuilding energy simulation models. Due to the rapid

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development of computers, it is possible that in thenear future, it will be possible to use 2-D, or even a 3-D heat transfer analysis as a standard module of building energy simulation tools.

Also, further research into the real world effects ofvarious window-wall interfaces can yield correlations or correction factors for use withperformance parameters determined by ratingprocedures. Such factors would improve software�sability to determine the absolute (as well as relative)energy impacts of fenestration products.

The NFRC rating system in the United States has made effective use of 2D heat transfer software to develop a cost-effective rating system. Thissystem�s effectiveness is in part due to the fact thatsince it is simulation based, it is easily integrated intothe product design process. This has led to an increase in the awareness of energy efficiency by manufacturers and an improvement in the energyefficiency of products manufactured. Similarsoftware could also be used to rate and evaluate wallsystems and other building components where betteraccounting for the impacts of thermal bridges isneeded.

REFERENCES1. Arasteh, D.K., Finlayson, E., Curcija, D.,

Baker, J., Huizenga, C., Guidelines formodeling projecting fenestration products,ASHRAE Transaction , Vol 104,Pt 1, 1998.

2. DOE2.1E Simulation Program, LawrenceBerkeley National Laboratory and Hirschand Associates, DOE-2 version 2.1e, 1994

3. EnergyPlus, Simulation Manual, LawrenceBerkeley National Laboratory, 2000.

4. Finlayson, E.U., Mitchell, R., Arasteh, D.,Huizenga, C., Curcija, D., THERM2.0.Program Description: A PC program foranalyzing two-dimensional heat transferthrough building products. LBL Report

37371. Lawrence Berkeley National Laboratory, Berkeley California, 2000.

5. Griffith, B., Curcija, D., Turler, D., Arasteh,D., Improving Computer Simulations ofHeat Transfer For Projecting FenestrationProducts: Using Radiation View FactorModels, ASHRAE Transactions, Vol. 104,Pt. 1, 1998.

6. Huizenga, C. Arasteh, D., Finlayson, R.,Mitchell, R., , and Curcija, D., THERM2.0.: A building component model for steady-state two-dimensional heat transfer, Proc.6th International IBPSA Conference,Building Simulation 99, Kyoto, 1999.

7. ISO 15099, "Window and doors - Thermaltransmission properties - Detailed calculations", TC163/WG2, InternationalStandard Organization,, Geneva,1998.

8. NFRC 100, Procedure for determiningfenestration product thermal properties(currently limited to U values), SilverSpring, MD, National Fenestration RatingCouncil, 1997.

9. Shapiro, A.B., FACET � A radiation viewfactor computer code for axi-symmetric, 2D planar and 3D geometries with shadowing,Lawrence Livermore National Laboratory,Rept UCID-19887, 1983

10. WINDOW 4.1 - A PC Program for Analyzing Window Thermal Performanceof Fenestration Products, LBL - 35298.Berkeley CA: Windows and DaylightingGroup, Lawrence Berkeley Laboratory,1994. LBL. 1996.

ACKNOWLEDGEMENTSThis work was supported by the Assistant Secretary for Energy Efficiency and Renewable Energy, Officeof Building Technology, State and CommunityPrograms, Office of Building Systems of the U.S. Department of Energy under Contracts No. DE-FC3-694CH10604, and DE-AC03-76SF00098.

Table 1: Thermo physical Properties of the material used in the analysis

Materialk (W/mK) e

Aluminum 160.0 0.2Polyurethane 0.03 0.9Polyisobutylene 0.24 0.9Silica Gel 0.03 0.9Silicone 0.36 0.9Wood (Pine) 0.14 0.9Steel-ANSI 1040 48.0 0.2Gypsum 0.016 0.9Insulation 0.043 0.9

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Table 2: Summary of resultsOverall heat transfer coefficient (U-factor) (W/m2K)

Cross section Whole windowWith detailed

radiationWithout detailed

radiationWith detailed

radiationWithout detailed

radiationIsolated window (hot boxinstallation)

2.46 2.68 1.98 2.04

Window/wall interface 3.56 3.94 2.19 2.28Window/room interface(vertical)

3.40 - 2.14 -

Window/room interface(horizontal)

3.30 - 2.12 -

Window/room interface and window at another wall also

3.26 - 2.11 -

Glazing System

Steel Spacer

Silica Gel

Polyurethane

Wood

Polysiobutylene(PIB)

Silicone

Frame Cavity

Aluminum

Figure 1. Cross Section of a Window Sill as Installed in Hot Box

Glazing (IGU)

Window Frame

Stool

Wood Studs

Apron

Gypsum Wall

Insulation

Wood Siding

Figure 2. Window in a Typical North American Frame Type Wall

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Figure 3. Window Location in a Room

Figure 4. Isotherms and U-factors For The Sill Cross Section

Exteriorboundarycondition

Interiorboundarycondition

Foam

Figure 5. Isotherms and U-Factors for Window Incorporated into Wall Assembly

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T=21.1oC

T=17.8o

T=17.8oC

Fig. 7: Simulation Model forWindow in a Vertical Position.

Fig 6: Isotherms and U-factors for Window ina Wall Assembly with Radiation Modeling

T=20oC

T=20oC

Window

Fig 8: Simulation Model for Window in a Horizontal Position

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Fig 9 : Typical Cross Section of Skylight

Fig 10 : : Isotherms and U-factors for Sill Cross Section in THERM with Radiation Model

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